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This assignment will strengthen the basic idea about the concept of the following distributions:
Assignment No: 2 (Lessons 27 – 30)
Question 1: Marks: 4+4=8
a) A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.
b) In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.
Question 2: Marks: 4+3=7
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STA301_Assignment_02_Solution
a).A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.
K = 4
N = 10
x = 2
n = 3
P(X=2) = 0.3 Ans
b).In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.
P = 0.36 Ans
n = 100 Ans
a).It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other. Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?
b).The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.
a).A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.
K = 4
N = 10
x = 2
n = 3
P(X=2) = 0.3 Ans
b).In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.
P = 0.36 Ans
n = 100 Ans
a).It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other. Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?
b).The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.
Question 1
a) A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.
Solution:
When n is greater then 5% of N the hyper geometric formula should be used.
Given:
K = 4
n = 3
N = 10
X = 2
putting these information in formula of hyper geometric
ans. is 0.3
Question 1:
a) In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.
Solution:
There is two parameters in binomial p.d. that is n and p and it’s generally denoted by b(x; n,p)
In binomial distribution Mean = E(x) = np
And S.D. =square root npq
Given:
Mean = np = 36
S.D. = = 4.8
Equations:
np = 36…………(1
square roor npq= 4.8………(2
For finding the value of n and p
First put the value of np in equation (2)
(square root q36) = 4.8
(root q)6 = 4.8
root q = 4.8/6
root q= 0.8
q = 0.64
We know that p+q = 1…………(3
For finding the value of ‘p’ put the value of q in equation (3)
P+ 0.64 = 1
P= 1- 0.64
P = 0.36
Now, for finding the value of ‘n’ put the value of p in equation (1)
np = 36
n(0.36)= 36
n = 36 / 0.36
n = 100
So,
p = 0.36
n = 100
Question 2: Marks: 4+3=7
is q mai hum binomial formula use kary gay kyon k poisson ki condition satisfy nai ho ri.
poisson k ly 'n' ka 20 say above hona zarori ha
so binomil lagao aur slove kar lo :)
question 2 (b) mai poisson process wala formula use ho ga kyon condition mai physical thing ki bat ho ri ha aur trails b independent hai
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